Minimizing NFA's and Regular Expressions [chapter]

Gregor Gramlich, Georg Schnitger
<span title="">2005</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We show inapproximability results concerning minimization of nondeterministic finite automata (nfa's) as well as regular expressions relative to given nfa's, regular expressions or deterministic finite automata (dfa's). We show that it is impossible to efficiently minimize a given nfa or regular expression with n states, transitions, resp. symbols within the factor o(n), unless P = PSPACE. Our inapproximability results for a given dfa with n states are based on cryptographic assumptions and we
more &raquo; ... how that any efficient algorithm will have an approximation factor of at least n poly(log n) . Our setup also allows us to analyze the minimum consistent dfa problem.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1007/978-3-540-31856-9_33</a> <a target="_blank" rel="external noopener" href="">fatcat:62akhfsipfc4vnp4t7skenc64e</a> </span>
<a target="_blank" rel="noopener" href="" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href=""> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> </button> </a>